icon-background-square
New
New
Year 9

Multiples of 10 involving negative exponents

I can write any integer in a range of forms.

icon-background-square
New
New
Year 9

Multiples of 10 involving negative exponents

I can write any integer in a range of forms.

warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

Lesson details

Key learning points

  1. A positive exponent tells you how many identical values must be multiplied together.
  2. Dividing by 10^n is the same as multiplying by its reciprocal.
  3. A negative exponent tells you how many reciprocals of the base must be multiplied together.
  4. a^(−3) = 1/a^3

Keywords

  • Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

Common misconception

A negative exponent implies that the entire value is negative.

Refer back to the table showing the structure of how the negative exponents occur and highlight that none of the decimal values are negative.


To help you plan your year 9 maths lesson on: Multiples of 10 involving negative exponents, download all teaching resources for free and adapt to suit your pupils' needs...

Ensure that you have place value grids accessible with the exponents of 10 included.
speech-bubble
Teacher tip
copyright

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

6 Questions

Q1.
A prime number is an integer greater than one with exactly factors.
Correct Answer: 2, two
Q2.
Which of the following products only use prime numbers?
Correct answer: 2 × 2 × 13
2 × 6 × 13
2 × 9 × 13
Correct answer: 2 × 3 × 5 × 17
Q3.
Write 300 as a product of its prime factors.
4 × 3 × 25
Correct answer: 2² × 3 × 5²
4 × 3 × 5²
2² × 3 × 25
2² × 3 × 5
Q4.
Use the fact that 60 = 2² × 3 × 5 to write 300 as a product of its prime factors.
2² × 3² × 5
Correct answer: 2² × 3 × 5²
2² × 3² × 5²
2 × 3 × 5²
Q5.
Use the fact that 60 = 2² × 3 × 5 to write 30 as a product of its prime factors.
2² × 3 × 5 ÷ 2
Correct answer: 2 × 3 × 5
2² × 5
2 × 3 × 5²
Q6.
If 52 = 2² × 13 and 175 = 5² × 7, which of the following is the most useful arrangement to calculate 175 × 52?
2 × 2 × 13 × 5 × 5 × 7
2 × 13 × 2 × 5 × 5 × 7
Correct answer: 2 × 5 × 2 × 5 × 13 × 7
2 × 7 × 2 × 5 × 13 × 5

6 Questions

Q1.
A number written in exponential form represents a repeated ...
addition
division
Correct answer: multiplication
subtraction
Q2.
Match each fraction to its equivalent exponential form.
Correct Answer:110,101
tick

101

Correct Answer:1100,102
tick

102

Correct Answer:11000,103
tick

103

Correct Answer:110000,104
tick

104

Correct Answer:1100000,105
tick

105

Correct Answer:11000000,106
tick

106

Q3.
Match each decimal to its equivalent exponential form.
Correct Answer:0.002,2×103
tick

2×103

Correct Answer:0.00004,4×105
tick

4×105

Correct Answer:0.2,2×101
tick

2×101

Correct Answer:0.005,5×103
tick

5×103

Correct Answer:0.000005,5×106
tick

5×106

Correct Answer:0.0004,4×104
tick

4×104

Q4.
3×102+2×105+8×106 represents the number
Correct Answer: 0.030028, 0.030 028
Q5.
Which of the following is not an alternative way of writing 2400?
24×102
24000÷10
Correct answer: 240000÷103
2.4×103
24010×102
Q6.
Which of the following is not an alternative way of writing 12 000?
Correct answer: 1.2×103
1200102×103
120000×101
1.2×104
Correct answer: 120103×104
This site uses cookies to store information on your computer. Some of these cookies are essential, while others help us to improve your experience by providing insights into how the site is being used.